How can I store and sync my work files in the cloud to access on my smartphone at home

"...have access of my own personal files from my work computer."

If you're talking about accessing your work from home, then - especially as a DoD contractor - you have no other choice but to ask IT/IS how. In this case, forgiveness IS NOT easier than permission, and loss of income is nothing if someone decides (thinks) that your attempts are malicious.

If you're talking about accessing your personal files on your work computer... I STRONGLY suggest you reconsider your goal. No good can come from that. NO good can come from that. NO GOOD can come from that. (Sorry... emphasis was needed.)

When you're doing a job for someone else, it's just not a good idea to mix business and personal work. Eventually, it will catch up to you, and the results can be painful.

You might want to check with your information security team. While the idea of what you are trying to do makes sense, it could violate the security policies. Most federal workplaces have policies that do not allow the electronic transmission of documents to a public or non-DOD controlled storage area like Dropbox, Google Drive, etc.

I would suggest if you need some storage for work files that can be accessed via the web i.e. laptop/pc, then I would try looking at AMRDEC-SAFE, it allows DoD members to share files up to 2 GB with other DoD members.

You might look at as milSuite and as I last heard, AKO had some storage features as well.
As far as syncing with your work computer, COL Vincent Stoneking may be onto something setting up a VM access.